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人気のある代数 >

0.3x^9-2.4=0

解

0.3 x^{9} - 2.4 = 0

解

x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i, x = 32 cos (\frac{2 π}{9}) + 32 i sin (\frac{2 π}{9}), x = 32 cos (\frac{8 π}{9}) + 32 i sin (\frac{8 π}{9}), x = 32 cos (\frac{14 π}{9}) + 32 i sin (\frac{14 π}{9}), x = 32 cos (\frac{2 π}{9}) - 32 i sin (\frac{2 π}{9}), x = 32 cos (\frac{4 π}{9}) + 32 i sin (\frac{4 π}{9}), x = 32 cos (\frac{10 π}{9}) + 32 i sin (\frac{10 π}{9})

解答ステップ

0.3 x^{9} - 2.4 = 0

2.4

を右側に移動します

0.3 x^{9} = 2.4

以下で両辺を割る

0.3

x^{9} = 8

equationを

u = x^{3}

と以下で書き換える:

u^{3} = x^{9}

u^{3} = 8

解く

u^{3} = 8 : u = 38, u = 38 \frac{- 1 + 3 i}{2}, u = 38 \frac{- 1 - 3 i}{2}

u = 38, u = 38 \frac{- 1 + 3 i}{2}, u = 38 \frac{- 1 - 3 i}{2}

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = 38 : x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i

解く

x^{3} = 38 \frac{- 1 + 3 i}{2} : x = 32 cos (\frac{2 π}{9}) + 32 i sin (\frac{2 π}{9}), x = 32 cos (\frac{8 π}{9}) + 32 i sin (\frac{8 π}{9}), x = 32 cos (\frac{14 π}{9}) + 32 i sin (\frac{14 π}{9})

解く

x^{3} = 38 \frac{- 1 - 3 i}{2} : x = 32 cos (\frac{2 π}{9}) - 32 i sin (\frac{2 π}{9}), x = 32 cos (\frac{4 π}{9}) + 32 i sin (\frac{4 π}{9}), x = 32 cos (\frac{10 π}{9}) + 32 i sin (\frac{10 π}{9})

解答は

x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i, x = 32 cos (\frac{2 π}{9}) + 32 i sin (\frac{2 π}{9}), x = 32 cos (\frac{8 π}{9}) + 32 i sin (\frac{8 π}{9}), x = 32 cos (\frac{14 π}{9}) + 32 i sin (\frac{14 π}{9}), x = 32 cos (\frac{2 π}{9}) - 32 i sin (\frac{2 π}{9}), x = 32 cos (\frac{4 π}{9}) + 32 i sin (\frac{4 π}{9}), x = 32 cos (\frac{10 π}{9}) + 32 i sin (\frac{10 π}{9})

グラフ

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